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<ul id="index">
  <li><a href="#NAME">NAME</a></li>
  <li><a href="#SYNOPSIS">SYNOPSIS</a></li>
  <li><a href="#DESCRIPTION">DESCRIPTION</a></li>
  <li><a href="#RETURN-VALUES">RETURN VALUES</a></li>
  <li><a href="#REMOVED-FUNCTIONALITY">REMOVED FUNCTIONALITY</a></li>
  <li><a href="#SEE-ALSO">SEE ALSO</a></li>
  <li><a href="#HISTORY">HISTORY</a></li>
  <li><a href="#COPYRIGHT">COPYRIGHT</a></li>
</ul>

<h1 id="NAME">NAME</h1>

<p>BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality</p>

<h1 id="SYNOPSIS">SYNOPSIS</h1>

<pre><code> <span class="comment">#include &lt;openssl/bn.h&gt;</span>
 
 <span class="keyword">int</span> <span class="variable">BN_generate_prime_ex</span><span class="operator">(</span><span class="variable">BIGNUM</span> <span class="variable">*ret</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">bits</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">safe</span><span class="operator">,</span> <span class="variable">const</span> <span class="variable">BIGNUM</span> <span class="variable">*add</span><span class="operator">,</span>
                          <span class="variable">const</span> <span class="variable">BIGNUM</span> <span class="variable">*rem</span><span class="operator">,</span> <span class="variable">BN_GENCB</span> <span class="variable">*cb</span><span class="operator">);</span>
 
 <span class="keyword">int</span> <span class="variable">BN_is_prime_ex</span><span class="operator">(</span><span class="variable">const</span> <span class="variable">BIGNUM</span> <span class="variable">*p</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">nchecks</span><span class="operator">,</span> <span class="variable">BN_CTX</span> <span class="variable">*ctx</span><span class="operator">,</span> <span class="variable">BN_GENCB</span> <span class="variable">*cb</span><span class="operator">);</span>
 
 <span class="keyword">int</span> <span class="variable">BN_is_prime_fasttest_ex</span><span class="operator">(</span><span class="variable">const</span> <span class="variable">BIGNUM</span> <span class="variable">*p</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">nchecks</span><span class="operator">,</span> <span class="variable">BN_CTX</span> <span class="variable">*ctx</span><span class="operator">,</span>
                             <span class="keyword">int</span> <span class="variable">do_trial_division</span><span class="operator">,</span> <span class="variable">BN_GENCB</span> <span class="variable">*cb</span><span class="operator">);</span>
 
 <span class="keyword">int</span> <span class="variable">BN_GENCB_call</span><span class="operator">(</span><span class="variable">BN_GENCB</span> <span class="variable">*cb</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">a</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">b</span><span class="operator">);</span>
 
 <span class="variable">BN_GENCB</span> <span class="variable">*BN_GENCB_new</span><span class="operator">(</span><span class="variable">void</span><span class="operator">);</span>
 
 <span class="variable">void</span> <span class="variable">BN_GENCB_free</span><span class="operator">(</span><span class="variable">BN_GENCB</span> <span class="variable">*cb</span><span class="operator">);</span>
 
 <span class="variable">void</span> <span class="variable">BN_GENCB_set_old</span><span class="operator">(</span><span class="variable">BN_GENCB</span> <span class="variable">*gencb</span><span class="operator">,</span>
                       <span class="variable">void</span> <span class="operator">(</span><span class="variable">*callback</span><span class="operator">)(</span><span class="keyword">int</span><span class="operator">,</span> <span class="keyword">int</span><span class="operator">,</span> <span class="variable">void</span> <span class="operator">*),</span> <span class="variable">void</span> <span class="variable">*cb_arg</span><span class="operator">);</span>
 
 <span class="variable">void</span> <span class="variable">BN_GENCB_set</span><span class="operator">(</span><span class="variable">BN_GENCB</span> <span class="variable">*gencb</span><span class="operator">,</span>
                   <span class="keyword">int</span> <span class="operator">(</span><span class="variable">*callback</span><span class="operator">)(</span><span class="keyword">int</span><span class="operator">,</span> <span class="keyword">int</span><span class="operator">,</span> <span class="variable">BN_GENCB</span> <span class="operator">*),</span> <span class="variable">void</span> <span class="variable">*cb_arg</span><span class="operator">);</span>
 
 <span class="variable">void</span> <span class="variable">*BN_GENCB_get_arg</span><span class="operator">(</span><span class="variable">BN_GENCB</span> <span class="variable">*cb</span><span class="operator">);</span>
</code></pre>

<p>Deprecated:</p>

<pre><code> <span class="comment">#if OPENSSL_API_COMPAT &lt; 0x00908000L</span>
 <span class="variable">BIGNUM</span> <span class="variable">*BN_generate_prime</span><span class="operator">(</span><span class="variable">BIGNUM</span> <span class="variable">*ret</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">num</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">safe</span><span class="operator">,</span> <span class="variable">BIGNUM</span> <span class="variable">*add</span><span class="operator">,</span>
                           <span class="variable">BIGNUM</span> <span class="variable">*rem</span><span class="operator">,</span> <span class="variable">void</span> <span class="operator">(</span><span class="variable">*callback</span><span class="operator">)(</span><span class="keyword">int</span><span class="operator">,</span> <span class="keyword">int</span><span class="operator">,</span> <span class="variable">void</span> <span class="operator">*),</span>
                           <span class="variable">void</span> <span class="variable">*cb_arg</span><span class="operator">);</span>
 
 <span class="keyword">int</span> <span class="variable">BN_is_prime</span><span class="operator">(</span><span class="variable">const</span> <span class="variable">BIGNUM</span> <span class="variable">*a</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">checks</span><span class="operator">,</span>
                 <span class="variable">void</span> <span class="operator">(</span><span class="variable">*callback</span><span class="operator">)(</span><span class="keyword">int</span><span class="operator">,</span> <span class="keyword">int</span><span class="operator">,</span> <span class="variable">void</span> <span class="operator">*),</span> <span class="variable">BN_CTX</span> <span class="variable">*ctx</span><span class="operator">,</span> <span class="variable">void</span> <span class="variable">*cb_arg</span><span class="operator">);</span>
 
 <span class="keyword">int</span> <span class="variable">BN_is_prime_fasttest</span><span class="operator">(</span><span class="variable">const</span> <span class="variable">BIGNUM</span> <span class="variable">*a</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">checks</span><span class="operator">,</span>
                          <span class="variable">void</span> <span class="operator">(</span><span class="variable">*callback</span><span class="operator">)(</span><span class="keyword">int</span><span class="operator">,</span> <span class="keyword">int</span><span class="operator">,</span> <span class="variable">void</span> <span class="operator">*),</span> <span class="variable">BN_CTX</span> <span class="variable">*ctx</span><span class="operator">,</span>
                          <span class="variable">void</span> <span class="variable">*cb_arg</span><span class="operator">,</span> <span class="keyword">int</span> <span class="variable">do_trial_division</span><span class="operator">);</span>
 <span class="comment">#endif</span>
</code></pre>

<h1 id="DESCRIPTION">DESCRIPTION</h1>

<p>BN_generate_prime_ex() generates a pseudo-random prime number of at least bit length <b>bits</b>. The returned number is probably prime with a negligible error.</p>

<p>If <b>ret</b> is not <b>NULL</b>, it will be used to store the number.</p>

<p>If <b>cb</b> is not <b>NULL</b>, it is used as follows:</p>

<ul>

<li><p><b>BN_GENCB_call(cb, 0, i)</b> is called after generating the i-th potential prime number.</p>

</li>
<li><p>While the number is being tested for primality, <b>BN_GENCB_call(cb, 1, j)</b> is called as described below.</p>

</li>
<li><p>When a prime has been found, <b>BN_GENCB_call(cb, 2, i)</b> is called.</p>

</li>
<li><p>The callers of BN_generate_prime_ex() may call <b>BN_GENCB_call(cb, i, j)</b> with other values as described in their respective man pages; see <a href="#SEE-ALSO">&quot;SEE ALSO&quot;</a>.</p>

</li>
</ul>

<p>The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange:</p>

<p>If <b>add</b> is not <b>NULL</b>, the prime will fulfill the condition p % <b>add</b> == <b>rem</b> (p % <b>add</b> == 1 if <b>rem</b> == <b>NULL</b>) in order to suit a given generator.</p>

<p>If <b>safe</b> is true, it will be a safe prime (i.e. a prime p so that (p-1)/2 is also prime).</p>

<p>The random generator must be seeded prior to calling BN_generate_prime_ex(). If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to external circumstances (see <a href="../man7/RAND.html">RAND(7)</a>), the operation will fail.</p>

<p>BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number <b>p</b> is prime. The following tests are performed until one of them shows that <b>p</b> is composite; if <b>p</b> passes all these tests, it is considered prime.</p>

<p>BN_is_prime_fasttest_ex(), when called with <b>do_trial_division == 1</b>, first attempts trial division by a number of small primes; if no divisors are found by this test and <b>cb</b> is not <b>NULL</b>, <b>BN_GENCB_call(cb, 1, -1)</b> is called. If <b>do_trial_division == 0</b>, this test is skipped.</p>

<p>Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin probabilistic primality test with <b>nchecks</b> iterations. If <b>nchecks == BN_prime_checks</b>, a number of iterations is used that yields a false positive rate of at most 2^-64 for random input. The error rate depends on the size of the prime and goes down for bigger primes. The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 2^-192 at 3747 bits and 2^-256 at 6394 bits.</p>

<p>When the source of the prime is not random or not trusted, the number of checks needs to be much higher to reach the same level of assurance: It should equal half of the targeted security level in bits (rounded up to the next integer if necessary). For instance, to reach the 128 bit security level, <b>nchecks</b> should be set to 64.</p>

<p>If <b>cb</b> is not <b>NULL</b>, <b>BN_GENCB_call(cb, 1, j)</b> is called after the j-th iteration (j = 0, 1, ...). <b>ctx</b> is a pre-allocated <b>BN_CTX</b> (to save the overhead of allocating and freeing the structure in a loop), or <b>NULL</b>.</p>

<p>BN_GENCB_call() calls the callback function held in the <b>BN_GENCB</b> structure and passes the ints <b>a</b> and <b>b</b> as arguments. There are two types of <b>BN_GENCB</b> structure that are supported: &quot;new&quot; style and &quot;old&quot; style. New programs should prefer the &quot;new&quot; style, whilst the &quot;old&quot; style is provided for backwards compatibility purposes.</p>

<p>A <b>BN_GENCB</b> structure should be created through a call to BN_GENCB_new(), and freed through a call to BN_GENCB_free().</p>

<p>For &quot;new&quot; style callbacks a BN_GENCB structure should be initialised with a call to BN_GENCB_set(), where <b>gencb</b> is a <b>BN_GENCB *</b>, <b>callback</b> is of type <b>int (*callback)(int, int, BN_GENCB *)</b> and <b>cb_arg</b> is a <b>void *</b>. &quot;Old&quot; style callbacks are the same except they are initialised with a call to BN_GENCB_set_old() and <b>callback</b> is of type <b>void (*callback)(int, int, void *)</b>.</p>

<p>A callback is invoked through a call to <b>BN_GENCB_call</b>. This will check the type of the callback and will invoke <b>callback(a, b, gencb)</b> for new style callbacks or <b>callback(a, b, cb_arg)</b> for old style.</p>

<p>It is possible to obtain the argument associated with a BN_GENCB structure (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.</p>

<p>BN_generate_prime() (deprecated) works in the same way as BN_generate_prime_ex() but expects an old-style callback function directly in the <b>callback</b> parameter, and an argument to pass to it in the <b>cb_arg</b>. BN_is_prime() and BN_is_prime_fasttest() can similarly be compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex(), respectively.</p>

<h1 id="RETURN-VALUES">RETURN VALUES</h1>

<p>BN_generate_prime_ex() return 1 on success or 0 on error.</p>

<p>BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is prime with an error probability of less than 0.25^<b>nchecks</b>, and -1 on error.</p>

<p>BN_generate_prime() returns the prime number on success, <b>NULL</b> otherwise.</p>

<p>BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or <b>NULL</b> otherwise.</p>

<p>BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB structure.</p>

<p>Callback functions should return 1 on success or 0 on error.</p>

<p>The error codes can be obtained by <a href="../man3/ERR_get_error.html">ERR_get_error(3)</a>.</p>

<h1 id="REMOVED-FUNCTIONALITY">REMOVED FUNCTIONALITY</h1>

<p>As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure directly, as in:</p>

<pre><code> <span class="variable">BN_GENCB</span> <span class="variable">callback</span><span class="operator">;</span>
</code></pre>

<p>Instead applications should create a BN_GENCB structure using BN_GENCB_new:</p>

<pre><code> <span class="variable">BN_GENCB</span> <span class="variable">*callback</span><span class="operator">;</span>
 <span class="variable">callback</span> <span class="operator">=</span> <span class="variable">BN_GENCB_new</span><span class="operator">();</span>
 <span class="keyword">if</span> <span class="operator">(!</span><span class="variable">callback</span><span class="operator">)</span>
     <span class="operator">/*</span> <span class="variable">error</span> <span class="operator">*/</span>
 <span class="operator">...</span>
 <span class="variable">BN_GENCB_free</span><span class="operator">(</span><span class="variable">callback</span><span class="operator">);</span>
</code></pre>

<h1 id="SEE-ALSO">SEE ALSO</h1>

<p><a href="../man3/DH_generate_parameters.html">DH_generate_parameters(3)</a>, <a href="../man3/DSA_generate_parameters.html">DSA_generate_parameters(3)</a>, <a href="../man3/RSA_generate_key.html">RSA_generate_key(3)</a>, <a href="../man3/ERR_get_error.html">ERR_get_error(3)</a>, <a href="../man3/RAND_bytes.html">RAND_bytes(3)</a>, <a href="../man7/RAND.html">RAND(7)</a></p>

<h1 id="HISTORY">HISTORY</h1>

<p>The BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.</p>

<h1 id="COPYRIGHT">COPYRIGHT</h1>

<p>Copyright 2000-2019 The OpenSSL Project Authors. All Rights Reserved.</p>

<p>Licensed under the OpenSSL license (the &quot;License&quot;). You may not use this file except in compliance with the License. You can obtain a copy in the file LICENSE in the source distribution or at <a href="https://www.openssl.org/source/license.html">https://www.openssl.org/source/license.html</a>.</p>


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